The classification of homogeneous scalar weighted shifts is known. Recently, Koranyi obtained a large class of inequivalent irreducible homogeneous bi-lateral 2-by-2 block shifts. We construct two distinct classes of examples not in the list of Koranyi. It is then shown that these new examples of irreducible homogeneous bi-lateral 2-by-2 block shifts, together with the ones found earlier by Koranyi, account for every unitarily inequivalent irreducible homogeneous bi-lateral 2-by-2 block shift.